document.write( "Question 441548: Again, I know there is not a section, but can anyone help with the following problem please?
\n" ); document.write( "Find the equation of the tangent line to the curve when x has the given value.\r
\n" ); document.write( "\n" ); document.write( "f(x) = x2 + 5x ; x = 4 \n" ); document.write( "

Algebra.Com's Answer #304747 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+f%28x%29+=+x2+%2B+5x+\"$
\n" ); document.write( "The derivative equation is
\n" ); document.write( " $\"+d1%28x%29+=+2x+%2B+5+\"$
\n" ); document.write( " $\"+d1%284%29+=+2%2A4+%2B+5+\"$
\n" ); document.write( " $\"+d1%284%29+=+13+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+f%284%29+=+4%5E2+%2B+5%2A4+\"$
\n" ); document.write( " $\"+f%284%29+=+16+%2B+20+\"$
\n" ); document.write( " $\"+f%284%29+=+36+\"$
\n" ); document.write( "Now I have a point, (4,36)
\n" ); document.write( "and the slope $\"+m+=+13+\"$
\n" ); document.write( " $\"+y+=+mx+%2B+b+\"$
\n" ); document.write( " $\"+y+=+13x+%2B+b+\"$
\n" ); document.write( " $\"+36+=+13%2A4+%2B+b+\"$
\n" ); document.write( " $\"+36+=+52+%2B+b+\"$
\n" ); document.write( " $\"+b+=+-16+\"$
\n" ); document.write( "The equation of the tangent is
\n" ); document.write( " $\"+y+=+13x+-+16+\"$
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+6%2C+-8%2C+44%2C+13x+-+16%2C+x%5E2+%2B+5x+%29+\"$ \n" ); document.write( "

\n" );